Sunday, November 26, 2006

The Beauty of it All

I can't say I was drawn to theoretical physics because I found it utterly beautiful. Indeed, I found physics in middle school extremely confusing and ugly. We were essentially presented a set of equations, and asked to measure or compute things without any apparent reason. I definitely preferred mathematics, where things seemed to have a relation to each other, and were build up on well defined and reliable axioms.

I was lucky though that I had a very patient teacher who tried to explain me that all these equations actually can be derived from common principles, just that the maths necessary for this was missing in 8th grade. (E.g. the factor 1/2 in the equation s = 1/2 g t2 suddenly makes sense, when you learn what integration and differentiation is.) I realized only much later that in most of her explanations she was actually talking about differential equations, and the variational principle - what I would call one of the most beautiful concepts in physics.

Some weeks ago I read an article in the October issue of Scientific American Mind "The Neurology of Aesthetics", which investigated the neurological causes of what humans find beautiful. This post is a very free interpretation of the article, and a comparably free relation to beauty in physics, since I don't think it is necessary to have college level maths skills to see the beauty of it all.

Symmetry/Broken Symmetry

The SciAm article states that allegedly we are attracted to symmetry because it is a property of 'most biological objects' and 'it pays to have an early warning system to draw your attention to symmetry [...] This attraction explains symmetries allure [...]'. Which I can't really agree on, because symmetry apparently is a feature also of non living objects, whereas there exist 'biological' objects that are a) not symmetrical but worth paying attention (don't worry if you can't read the text, I'm still feeling slightly sick), or b) symmetrical but doubtful in their aesthetic value (don't click if you suffer from arachnophobia). But whatever the neurological reason, symmetry is mostly considered as beautiful, which is also the case in physics:

There are the obvious examples of crystal growth (see here for more snowflakes) which are based on lattices. Then there is the power of symmetries to classify a confusing amount of particles: the quark model, a brilliant example of how symmetries (in this case SU(3)) allow to explain the observed particle zoo by building them up of only some few constituents. (See here for more info about the Eightfold Way).

The pictures below show probability distributions of electrons in the hydrogen atom, as one can compute with elementary quantum mechanics (pictures drawn with this applet, if you want to play around).

The principle of symmetries finds its most powerful application in gauge symmetries, which are the foundation of the standard model of particle physics.

However, as my mother likes to say 'Symmetrie ist die Kunst der Blöden.' -- 'Symmetry is the art of the poor.' Which is true in the sense that perfect symmetry is just boring. From the photos at the beginning of this section, none has perfect symmetry. The breaking of symmetries is essential to the formation of life. It is what makes nature an interesting place.

Patterns and Structures

The left picture above shows a piece of the Cosmic Microwave Background, the results from the WMAP measurements. From the sizes and colors (temperature fluctuation) of this pattern one can extract information about the structures at the time of radiation-matter equality.

Another example for structures in physics is closely connected to the search for a theory of quantum gravity. It is generally expected that at smallest scales (close by the Planck length) the spacetime we sit in is not a smooth background but quite messy and quantum foamy, see e.g. here for a picture and a brief introduction.

Less is More

Simplification is one of the primary goals in theoretical physics. Basically the whole search for a theory of everything can be thought of as a search for simplification. Some of the most compelling examples for a successful simplification are maybe the unification of (classical) electric and magnetic phenomena in Maxwell's equations, and the quantum field theory of electro-weak interactions.

But simplification is not only a goal. It is also an useful tool. Think about describing the properties of vapor. You don't compute the motions of every single atom, instead you describe the whole system by some few properties like temperature, pressure and volume.

Another well known example is considering the cow to be a sphere. This might be quite a crude approximation of you think about said cow as your next dinner. But If you want to describe, say, how a cow drops out of a plane and hit some innocent fisherman, it's completely appropriate to describe it as a sphere.

Simplification is also behind the cosmological principle, according to which the universe is roughly the same everywhere, and looks the same in every direction. This sounds pretty silly if you look at the screen in front of you, but makes sense if you think of galaxies as particles in a cosmic fluid. The CMB structures shown above are departures from this over-simplified description.

Besides being beautiful, simplification is an extremely powerful concept that can save a lot of brain time.


The SciAm article refers to this as 'hypernormal stimuli': an amplified reaction to unusual modifications of a certain property, like high contrast colors, exaggerated shapes etc. They write 'We do not know why this effect occurs but it probably results from the way in which visual neurons encode sensory information' (Which imho is equivalent to saying they don't know anything.)

To come to theoretical physics, it seems that humans are just fascinated by strange thought experiments like: What would happen if you could travel at, or even faster than the speed of light? If you fell into a black hole? If the electron mass was only a bit larger? If space-time was made of braids? What if you'd try to microwave a marshmallow? Describe everything as tiny vibrating strings? What if you could fly? Travel back in time?

There's no doubt physicists like extremes.

Problem Solving

I was kind of surprised to see the SciAm article listing problem solving as a factor for beauty, the reason being 'When the correct fragments click into place, we feel a gratifying 'aha'.' This doesn't only make us like the picture whose 'problem we solved', but it is essentially what physics is all about: explaining the underlying concepts of things that look puzzling at first sight.

Another nice example for the fascination caused by problems are maybe also Esher's impossible pictures.

An additional point that doesn't relate to beauty in theoretical physics is that of a visual metaphor which draws its relevance from the historical and sociological context.

And if you want to get a perspective of how our concept of beauty is affected through the media, look at this video.

    Don’t the hours grow shorter as the days go by
    We never get to stop and open our eyes
    One minute you’re waiting for the sky to fall
    The next you’re dazzled by the beauty of it all

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  1. The problem is that you can't say, 'Hey, what would happen if you could go faster than the speed of light?' because that's totally physically impossible. It's not possible to go faster than the speed of light, so the laws of physics can't possibly say what would happen if you imagine things that way in some hypothetical universe. Physics is a complete package: once you decide to ignore one physical law, you're ignoring them all.

    So does that mean no pockets universes where the laws of physics are different?
    An oddly enough, when we look at other galaxies are we not assuming that they obey certain laws of physics? - as we know them
    One could have assumed neutrinos did not exist or even were not possible according to the laws of physics as were known 100 years ago - one could even have assumed a controlled nuclear explosion could not be created 50 years before the first one.

    Do we not every day strip off layers of previous physical and/or theoretical limitations.

    Hmmm it seems most insects still haven't learnt how to avoid a car at 50 mph never mind 150 mph
    Yet 'most' birds have learnt to avoid planes at 600 mph or faster

    So what is the theoretical fastest a pilotless plane or missile can fly - today?

    Now, I am not saying we can make anything with any mass or significant volume (size) travel faster than light - but where are the limits?

    Nor can we drive a car thru a built up city at 200 mph - but we can go even faster on race tracks

  2. Dear Bee,

    a very beautiful post, and one which gives a lot to ponder :-) As always, your choice of pictures and links is just amazing!

    Best, stefan

  3. PS - Bee, I second Stefan
    Great post, great pics, great links

  4. Hi Quasar,

    Thanks :-) Regarding your 1st comment: I didn't link to the site because I share their opinion, but because I meant to underline that questions like this are just fascinating: a game of mind, a thought experiment, they captures our imagination and occupy our dreams. If you don't know it, I can recommend Joao's book

    Faster Than the Speed of Light



    PS: *lol* I just saw that lists Lee's book on top of my recommendation list :-)

  5. Yes I enjoyed this post very much too.

    A "1 inch" equation is always nice for sure. Entropically "matter distinctions" can become very complex. Where did they arise from?

    Doesn't this set up certain assumptions on it's own?

    The butterfly is the animal that is regularly given as one of the most beautiful examples of bilateral symmetry in the natural world.

  6. Good post!

    The last video was on a different wavelength from all the rest, in my opinion. It is as though you suddenly pushed the reader into a different area of the Landscape. Or is the photoshopped face on the billboard another aspect of the false coloring we do to visualize the cosmic background radiation? and all the apparatus we use to look at the universe?

    "Every universe should feel beautiful as it is without human manipulation!"


  7. Hi Arun,

    The last video, the one from the Barenaked Ladies? I guess you mean the Dove-video?

    as though you suddenly pushed the reader into a different area of the Landscape. Or is the photoshopped face on the billboard another aspect of the false coloring we do to visualize the cosmic background radiation? and all the apparatus we use to look at the universe?

    Well yes, I admit I was looking for a reason to link to the video. But its meant to say that our perception of beauty is affected by the world we live in. If you advertise cleverly, you might be able to amplify the good points, and cover the not-so good points. It doesn't change anything about what you are trying to sell, but it might convince more people to buy it.



  8. The problem is that you can't say, 'Hey, what would happen if you could go faster than the speed of light?' because that's totally physically impossible.... Physics is a complete package: once you decide to ignore one physical law, you're ignoring them all.

    Nonsense! The cosmic speed limit is no more immutable than CP symmetry, Newton's second law, and the massless neutrino. It's a good thing people wondered what would happen if these laws were ignored -- otherwise, we never would've recognized CP violation, relativistic mass, and neutrino oscillations when we saw them!

  9. Nonsense! The cosmic speed limit is no more immutable than CP symmetry, Newton's second law, and the massless neutrino

    Strong words...

    But it seems to me that your examples differ quite a lot in the degree to which possible deviations of these "laws" are hard-wired to other areas of physics.

    I mean, you may introduce a neutrino mass in the standard model with some extra terms and have to think about the Higgs sector. On the other hand, the speed limit is quite fundamental, so its violation would appear quite ad hoc and arbitrary, since I guess you would not like to throw away anything that comes with Poincare symmetry? That's in fact one problem I personally have with the DSR approach...

    Best, stefan

  10. I don't know for sure why this comment section developed into a discussion about the speed of light, but cosmic coincidence or not, I've twisted my brain most of today about this issue. Here's a question:

    There is a parameter in the Lorentz-transformation which is 'c'. How precisely do we actually know this speed is the speed of light? Can we make the speed of light energy dependent (see e.g. The Minimal Length) if it's not the parameter in the trafos? To me it seems so. The reason being that it's actually the energy-momentum relation (alias dispersion relation) that sets the speed of light to be constant, not the Lorentz transformation. In such a scenario, the speed of light would always be larger than 'c' in the Lorentz trafo, though for energies much smaller than the Planck scale one wouldn't notice.

    Does anybody notice apparent inconsistencies?

    That doesn't solve my problem, but at least it makes somewhat sense to me.

  11. Great post! I tried to comment the other day, but blogger was down.

  12. re: symmetry and broken symmetry.

    The epigraph to Chandrasekhar's The Mathematical Theory of Black Holes has a couple of quotes (from memory since the book is at work, and I'm not):

    Heisenberg: Beauty consists of the proper proportion of the parts to the whole, and to each other.

    Bacon: There is no thing of excellent beauty that hath not some strangeness in the proportion

  13. Hi CIP,

    Thanks for the quotations! I esp. like the one by Bacon, perfect symmetry is just boring, it's the mastery of breaking the symmetry that succeeds to cause all the beauty of life. Best,


  14. "Lovers In A Dangerous Time" is by Bruce Cockburn, not The Barenaked Ladies.

  15. Hi Docatonic,

    True, thanks for adding that info. What was humming in my head however was the version from TBN. Best,



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